vicinity of the extra atomic rows. The dislocations interrupt the basic cell arrangement corresponding to the equilibrium condition shown in Fig. 10.8a. The red circles indicate the intersections of the plane of the image with the spherical regions that correspond to the equilibrium positions. The intensity distributions within these circles are functions of the electron density with the maxima in correspondence with the nuclei of the atoms. The atoms positions are outlined by the corresponding circles with the exception of the atoms just after the extra-rows end indicated by yellow circles in Fig. 10.14a and outlined by yellow dots in Fig. 10.6b. These images show high intensity with little variation like blurred images. Just behind this atoms row there is a region of very low light intensity indicating a low density of the electron field. This region interrupts the sequence of the hexagonal patterns corresponding to the equilibrium positions of the atoms and is outlined with green dots. This region is the beginning of a sort of cavity that is almost located in the intersection of the yellow lines defining the orientation of the extra-rows. The next row of atoms, close to the yellow lines shows a deformation in the direction of the Burger’s vector, <1120 >of approximately εe ¼0.130. Figure 10.14b shows the packing of rigid magnetic spheres. It is possible to see that the model of attracting rigid spheres, although an interesting visualization for an edge dislocation, does not provide the actual field of atomic arrangement. Atoms evidently cannot be modeled as rigid spheres: the cavity in the dislocation region of the rigid spheres is about 6.5ro long while in the actual dislocation is roughly about 2ro, and actually it is not a cavity in the strict sense of the word as the image shows the presence of some electron density in the cavity. The cavities formed between atoms due to the presence of structural defects have an interesting property that makes its presence experimentally detectable. Due to the low electronic density if positrons are sent to this cavity, an electron and a positron form a pair, this pair is not stable and decays into two γ-rays. Using a γ-rays detector it is possible to count the number of events and this number can be used to provide a measure the number of cavities present in a specimen [28]. It is interesting to notice here that the application of the Cauchy-Born rule as a homogenization technique provides a displacement field that yields high derivative values indicating the presence of a dislocation and merges with the theory of elasticity modeling of an edge dislocation. The problem that the molecular dynamics attempts to solve is the problem of the instability of the molecular arrangement that leads to the actual onset of plasticity and eventually to the fracture of the crystal. From Fig. 10.13, it can be concluded that the elasticity solution of an edge dislocation mimics what actually occurs at an actual dislocation: there is a region with very high compressive strains (the main parameters of the elementary cells are shortened), followed by a neutral region where the atoms remain in the equilibrium configuration (no deformation occurs), followed by a region where the basic parameters of the elementary cell are increased (tension region). However, while the theory of elasticity provides symmetrical compression and tension regions, the experimental results shows that these two regions are not symmetric due to the property of the modulus of elasticity as a derivative of the potential energy (see Fig. 10.2b), which is not symmetric with respect to the equilibrium position. It is important to realize that the observed image is a snap shot of events that occur in time. For example, the blurred images of the electronic density after the extra atomic rows end could mean that the electronic density fluctuates during the picture exposure time due to the energy imparted by the electron beam of the microscope to the atoms located at the dislocation edge [22]. 10.13 Discussion and Conclusions The main objective of this paper was to utilize Experimental Mechanics methods to establish a bridge between classical continuum mechanics variables and the atomistic analysis of solid mechanics, thus providing experimental evidence that supports the Cauchy-Born conjecture and shedding light on the connection between atomic configuration changes and continuum mechanics solutions as homogenizing functions of these changes. There are two important aspects to this problem, the description of the motion of the continuum in function of a parameter (for example, the time), the kinematics of the continuum. The other fundamental aspect is the dynamics of the motion, the connection of the kinematic variables with the forces that cause the motion. This paper has focused on the kinematics of atomic motions and its connection with the kinematics of the continuum. The fundamental question that is investigated is the connection between the phenomenological description of the deformation of solids by Continuum Mechanics and the basic geometrical changes that take place at the level of crystalline organization. The basic question that the theoretical efforts of atomistic based models as well as the Continuum approach try to answer has deeper practical consequences for scientists and engineers: Which are the mechanisms of atomic configurations or of the parameters of the Continuum approach that lead to the fracture of crystals? In simple words, a reiteration of centuries old question: Why things fracture, why things fail? Throughout centuries multiple paths have been followed to get partial 96 C.A. Sciammarella et al.
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